/*
 * Copyright 2002 Niels Provos <provos@citi.umich.edu>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

#ifndef _SYS_TREE_H_
#define _SYS_TREE_H_

/*
 * This file defines data structures for different types of trees:
 * splay trees and red-black trees.
 *
 * A splay tree is a self-organizing data structure.  Every operation
 * on the tree causes a splay to happen.  The splay moves the requested
 * node to the root of the tree and partly rebalances it.
 *
 * This has the benefit that request locality causes faster lookups as
 * the requested nodes move to the top of the tree.  On the other hand,
 * every lookup causes memory writes.
 *
 * The Balance Theorem bounds the total access time for m operations
 * and n inserts on an initially empty tree as O((m + n)lg n).  The
 * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
 *
 * A red-black tree is a binary search tree with the node color as an
 * extra attribute.  It fulfills a set of conditions:
 *  - every search path from the root to a leaf consists of the
 *    same number of black nodes,
 *  - each red node (except for the root) has a black parent,
 *  - each leaf node is black.
 *
 * Every operation on a red-black tree is bounded as O(lg n).
 * The maximum height of a red-black tree is 2lg (n+1).
 */

#define SPLAY_HEAD(name, type)                    \
  struct name {                                   \
    struct type* sph_root; /* root of the tree */ \
  }

#define SPLAY_INITIALIZER(root) \
  { NULL }

#define SPLAY_INIT(root)     \
  do {                       \
    (root)->sph_root = NULL; \
  } while (0)

#define SPLAY_ENTRY(type)                       \
  struct {                                      \
    struct type* spe_left;  /* left element */  \
    struct type* spe_right; /* right element */ \
  }

#define SPLAY_LEFT(elm, field) (elm)->field.spe_left
#define SPLAY_RIGHT(elm, field) (elm)->field.spe_right
#define SPLAY_ROOT(head) (head)->sph_root
#define SPLAY_EMPTY(head) (SPLAY_ROOT(head) == NULL)

/* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
#define SPLAY_ROTATE_RIGHT(head, tmp, field)                       \
  do {                                                             \
    SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field); \
    SPLAY_RIGHT(tmp, field) = (head)->sph_root;                    \
    (head)->sph_root = tmp;                                        \
  } while (0)

#define SPLAY_ROTATE_LEFT(head, tmp, field)                        \
  do {                                                             \
    SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field); \
    SPLAY_LEFT(tmp, field) = (head)->sph_root;                     \
    (head)->sph_root = tmp;                                        \
  } while (0)

#define SPLAY_LINKLEFT(head, tmp, field)                    \
  do {                                                      \
    SPLAY_LEFT(tmp, field) = (head)->sph_root;              \
    tmp = (head)->sph_root;                                 \
    (head)->sph_root = SPLAY_LEFT((head)->sph_root, field); \
  } while (0)

#define SPLAY_LINKRIGHT(head, tmp, field)                    \
  do {                                                       \
    SPLAY_RIGHT(tmp, field) = (head)->sph_root;              \
    tmp = (head)->sph_root;                                  \
    (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field); \
  } while (0)

#define SPLAY_ASSEMBLE(head, node, left, right, field)               \
  do {                                                               \
    SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);  \
    SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field); \
    SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);  \
    SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);  \
  } while (0)

/* Generates prototypes and inline functions */

#define SPLAY_PROTOTYPE(name, type, field, cmp)                        \
  void name##_SPLAY(struct name*, struct type*);                       \
  void name##_SPLAY_MINMAX(struct name*, int);                         \
  struct type* name##_SPLAY_INSERT(struct name*, struct type*);        \
  struct type* name##_SPLAY_REMOVE(struct name*, struct type*);        \
                                                                       \
  /* Finds the node with the same key as elm */                        \
  static __inline struct type* name##_SPLAY_FIND(struct name* head,    \
                                                 struct type* elm) {   \
    if (SPLAY_EMPTY(head)) return (NULL);                              \
    name##_SPLAY(head, elm);                                           \
    if ((cmp)(elm, (head)->sph_root) == 0) return (head->sph_root);    \
    return (NULL);                                                     \
  }                                                                    \
                                                                       \
  static __inline struct type* name##_SPLAY_NEXT(struct name* head,    \
                                                 struct type* elm) {   \
    name##_SPLAY(head, elm);                                           \
    if (SPLAY_RIGHT(elm, field) != NULL) {                             \
      elm = SPLAY_RIGHT(elm, field);                                   \
      while (SPLAY_LEFT(elm, field) != NULL) {                         \
        elm = SPLAY_LEFT(elm, field);                                  \
      }                                                                \
    } else                                                             \
      elm = NULL;                                                      \
    return (elm);                                                      \
  }                                                                    \
                                                                       \
  static __inline struct type* name##_SPLAY_MIN_MAX(struct name* head, \
                                                    int val) {         \
    name##_SPLAY_MINMAX(head, val);                                    \
    return (SPLAY_ROOT(head));                                         \
  }

/* Main splay operation.
 * Moves node close to the key of elm to top
 */
#define SPLAY_GENERATE(name, type, field, cmp)                            \
  struct type* name##_SPLAY_INSERT(struct name* head, struct type* elm) { \
    if (SPLAY_EMPTY(head)) {                                              \
      SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;            \
    } else {                                                              \
      int __comp;                                                         \
      name##_SPLAY(head, elm);                                            \
      __comp = (cmp)(elm, (head)->sph_root);                              \
      if (__comp < 0) {                                                   \
        SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);     \
        SPLAY_RIGHT(elm, field) = (head)->sph_root;                       \
        SPLAY_LEFT((head)->sph_root, field) = NULL;                       \
      } else if (__comp > 0) {                                            \
        SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field);   \
        SPLAY_LEFT(elm, field) = (head)->sph_root;                        \
        SPLAY_RIGHT((head)->sph_root, field) = NULL;                      \
      } else                                                              \
        return ((head)->sph_root);                                        \
    }                                                                     \
    (head)->sph_root = (elm);                                             \
    return (NULL);                                                        \
  }                                                                       \
                                                                          \
  struct type* name##_SPLAY_REMOVE(struct name* head, struct type* elm) { \
    struct type* __tmp;                                                   \
    if (SPLAY_EMPTY(head)) return (NULL);                                 \
    name##_SPLAY(head, elm);                                              \
    if ((cmp)(elm, (head)->sph_root) == 0) {                              \
      if (SPLAY_LEFT((head)->sph_root, field) == NULL) {                  \
        (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);          \
      } else {                                                            \
        __tmp = SPLAY_RIGHT((head)->sph_root, field);                     \
        (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);           \
        name##_SPLAY(head, elm);                                          \
        SPLAY_RIGHT((head)->sph_root, field) = __tmp;                     \
      }                                                                   \
      return (elm);                                                       \
    }                                                                     \
    return (NULL);                                                        \
  }                                                                       \
                                                                          \
  void name##_SPLAY(struct name* head, struct type* elm) {                \
    struct type __node, *__left, *__right, *__tmp;                        \
    int __comp;                                                           \
                                                                          \
    SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;      \
    __left = __right = &__node;                                           \
                                                                          \
    while ((__comp = (cmp)(elm, (head)->sph_root))) {                     \
      if (__comp < 0) {                                                   \
        __tmp = SPLAY_LEFT((head)->sph_root, field);                      \
        if (__tmp == NULL) break;                                         \
        if ((cmp)(elm, __tmp) < 0) {                                      \
          SPLAY_ROTATE_RIGHT(head, __tmp, field);                         \
          if (SPLAY_LEFT((head)->sph_root, field) == NULL) break;         \
        }                                                                 \
        SPLAY_LINKLEFT(head, __right, field);                             \
      } else if (__comp > 0) {                                            \
        __tmp = SPLAY_RIGHT((head)->sph_root, field);                     \
        if (__tmp == NULL) break;                                         \
        if ((cmp)(elm, __tmp) > 0) {                                      \
          SPLAY_ROTATE_LEFT(head, __tmp, field);                          \
          if (SPLAY_RIGHT((head)->sph_root, field) == NULL) break;        \
        }                                                                 \
        SPLAY_LINKRIGHT(head, __left, field);                             \
      }                                                                   \
    }                                                                     \
    SPLAY_ASSEMBLE(head, &__node, __left, __right, field);                \
  }                                                                       \
                                                                          \
  /* Splay with either the minimum or the maximum element                 \
   * Used to find minimum or maximum element in tree.                     \
   */                                                                     \
  void name##_SPLAY_MINMAX(struct name* head, int __comp) {               \
    struct type __node, *__left, *__right, *__tmp;                        \
                                                                          \
    SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;      \
    __left = __right = &__node;                                           \
                                                                          \
    while (1) {                                                           \
      if (__comp < 0) {                                                   \
        __tmp = SPLAY_LEFT((head)->sph_root, field);                      \
        if (__tmp == NULL) break;                                         \
        if (__comp < 0) {                                                 \
          SPLAY_ROTATE_RIGHT(head, __tmp, field);                         \
          if (SPLAY_LEFT((head)->sph_root, field) == NULL) break;         \
        }                                                                 \
        SPLAY_LINKLEFT(head, __right, field);                             \
      } else if (__comp > 0) {                                            \
        __tmp = SPLAY_RIGHT((head)->sph_root, field);                     \
        if (__tmp == NULL) break;                                         \
        if (__comp > 0) {                                                 \
          SPLAY_ROTATE_LEFT(head, __tmp, field);                          \
          if (SPLAY_RIGHT((head)->sph_root, field) == NULL) break;        \
        }                                                                 \
        SPLAY_LINKRIGHT(head, __left, field);                             \
      }                                                                   \
    }                                                                     \
    SPLAY_ASSEMBLE(head, &__node, __left, __right, field);                \
  }

#define SPLAY_NEGINF -1
#define SPLAY_INF 1

#define SPLAY_INSERT(name, x, y) name##_SPLAY_INSERT(x, y)
#define SPLAY_REMOVE(name, x, y) name##_SPLAY_REMOVE(x, y)
#define SPLAY_FIND(name, x, y) name##_SPLAY_FIND(x, y)
#define SPLAY_NEXT(name, x, y) name##_SPLAY_NEXT(x, y)
#define SPLAY_MIN(name, x) \
  (SPLAY_EMPTY(x) ? NULL : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
#define SPLAY_MAX(name, x) \
  (SPLAY_EMPTY(x) ? NULL : name##_SPLAY_MIN_MAX(x, SPLAY_INF))

#define SPLAY_FOREACH(x, name, head)             \
  for ((x) = SPLAY_MIN(name, head); (x) != NULL; \
       (x) = SPLAY_NEXT(name, head, x))

/* Macros that define a red-back tree */
#define RB_HEAD(name, type)                       \
  struct name {                                   \
    struct type* rbh_root; /* root of the tree */ \
  }

#define RB_INITIALIZER(root) \
  { NULL }

#define RB_INIT(root)        \
  do {                       \
    (root)->rbh_root = NULL; \
  } while (0)

#define RB_BLACK 0
#define RB_RED 1
#define RB_ENTRY(type)                            \
  struct {                                        \
    struct type* rbe_left;   /* left element */   \
    struct type* rbe_right;  /* right element */  \
    struct type* rbe_parent; /* parent element */ \
    int rbe_color;           /* node color */     \
  }

#define RB_LEFT(elm, field) (elm)->field.rbe_left
#define RB_RIGHT(elm, field) (elm)->field.rbe_right
#define RB_PARENT(elm, field) (elm)->field.rbe_parent
#define RB_COLOR(elm, field) (elm)->field.rbe_color
#define RB_ROOT(head) (head)->rbh_root
#define RB_EMPTY(head) (RB_ROOT(head) == NULL)

#define RB_SET(elm, parent, field)                     \
  do {                                                 \
    RB_PARENT(elm, field) = parent;                    \
    RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \
    RB_COLOR(elm, field) = RB_RED;                     \
  } while (0)

#define RB_SET_BLACKRED(black, red, field) \
  do {                                     \
    RB_COLOR(black, field) = RB_BLACK;     \
    RB_COLOR(red, field) = RB_RED;         \
  } while (0)

#ifndef RB_AUGMENT
#define RB_AUGMENT(x)
#endif

#define RB_ROTATE_LEFT(head, elm, tmp, field)                       \
  do {                                                              \
    (tmp) = RB_RIGHT(elm, field);                                   \
    if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field))) {             \
      RB_PARENT(RB_LEFT(tmp, field), field) = (elm);                \
    }                                                               \
    RB_AUGMENT(elm);                                                \
    if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {          \
      if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))           \
        RB_LEFT(RB_PARENT(elm, field), field) = (tmp);              \
      else                                                          \
        RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);             \
    } else                                                          \
      (head)->rbh_root = (tmp);                                     \
    RB_LEFT(tmp, field) = (elm);                                    \
    RB_PARENT(elm, field) = (tmp);                                  \
    RB_AUGMENT(tmp);                                                \
    if ((RB_PARENT(tmp, field))) RB_AUGMENT(RB_PARENT(tmp, field)); \
  } while (0)

#define RB_ROTATE_RIGHT(head, elm, tmp, field)                      \
  do {                                                              \
    (tmp) = RB_LEFT(elm, field);                                    \
    if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field))) {             \
      RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);               \
    }                                                               \
    RB_AUGMENT(elm);                                                \
    if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field))) {          \
      if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))           \
        RB_LEFT(RB_PARENT(elm, field), field) = (tmp);              \
      else                                                          \
        RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);             \
    } else                                                          \
      (head)->rbh_root = (tmp);                                     \
    RB_RIGHT(tmp, field) = (elm);                                   \
    RB_PARENT(elm, field) = (tmp);                                  \
    RB_AUGMENT(tmp);                                                \
    if ((RB_PARENT(tmp, field))) RB_AUGMENT(RB_PARENT(tmp, field)); \
  } while (0)

/* Generates prototypes and inline functions */
#define RB_PROTOTYPE(name, type, field, cmp)                             \
  void name##_RB_INSERT_COLOR(struct name*, struct type*);               \
  void name##_RB_REMOVE_COLOR(struct name*, struct type*, struct type*); \
  struct type* name##_RB_REMOVE(struct name*, struct type*);             \
  struct type* name##_RB_INSERT(struct name*, struct type*);             \
  struct type* name##_RB_FIND(struct name*, struct type*);               \
  struct type* name##_RB_NEXT(struct type*);                             \
  struct type* name##_RB_MINMAX(struct name*, int);

/* Main rb operation.
 * Moves node close to the key of elm to top
 */
#define RB_GENERATE(name, type, field, cmp)                                   \
  void name##_RB_INSERT_COLOR(struct name* head, struct type* elm) {          \
    struct type *parent, *gparent, *tmp;                                      \
    while ((parent = RB_PARENT(elm, field)) &&                                \
           RB_COLOR(parent, field) == RB_RED) {                               \
      gparent = RB_PARENT(parent, field);                                     \
      if (parent == RB_LEFT(gparent, field)) {                                \
        tmp = RB_RIGHT(gparent, field);                                       \
        if (tmp && RB_COLOR(tmp, field) == RB_RED) {                          \
          RB_COLOR(tmp, field) = RB_BLACK;                                    \
          RB_SET_BLACKRED(parent, gparent, field);                            \
          elm = gparent;                                                      \
          continue;                                                           \
        }                                                                     \
        if (RB_RIGHT(parent, field) == elm) {                                 \
          RB_ROTATE_LEFT(head, parent, tmp, field);                           \
          tmp = parent;                                                       \
          parent = elm;                                                       \
          elm = tmp;                                                          \
        }                                                                     \
        RB_SET_BLACKRED(parent, gparent, field);                              \
        RB_ROTATE_RIGHT(head, gparent, tmp, field);                           \
      } else {                                                                \
        tmp = RB_LEFT(gparent, field);                                        \
        if (tmp && RB_COLOR(tmp, field) == RB_RED) {                          \
          RB_COLOR(tmp, field) = RB_BLACK;                                    \
          RB_SET_BLACKRED(parent, gparent, field);                            \
          elm = gparent;                                                      \
          continue;                                                           \
        }                                                                     \
        if (RB_LEFT(parent, field) == elm) {                                  \
          RB_ROTATE_RIGHT(head, parent, tmp, field);                          \
          tmp = parent;                                                       \
          parent = elm;                                                       \
          elm = tmp;                                                          \
        }                                                                     \
        RB_SET_BLACKRED(parent, gparent, field);                              \
        RB_ROTATE_LEFT(head, gparent, tmp, field);                            \
      }                                                                       \
    }                                                                         \
    RB_COLOR(head->rbh_root, field) = RB_BLACK;                               \
  }                                                                           \
                                                                              \
  void name##_RB_REMOVE_COLOR(struct name* head, struct type* parent,         \
                              struct type* elm) {                             \
    struct type* tmp;                                                         \
    while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) &&               \
           elm != RB_ROOT(head)) {                                            \
      if (RB_LEFT(parent, field) == elm) {                                    \
        tmp = RB_RIGHT(parent, field);                                        \
        if (RB_COLOR(tmp, field) == RB_RED) {                                 \
          RB_SET_BLACKRED(tmp, parent, field);                                \
          RB_ROTATE_LEFT(head, parent, tmp, field);                           \
          tmp = RB_RIGHT(parent, field);                                      \
        }                                                                     \
        if ((RB_LEFT(tmp, field) == NULL ||                                   \
             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&             \
            (RB_RIGHT(tmp, field) == NULL ||                                  \
             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {            \
          RB_COLOR(tmp, field) = RB_RED;                                      \
          elm = parent;                                                       \
          parent = RB_PARENT(elm, field);                                     \
        } else {                                                              \
          if (RB_RIGHT(tmp, field) == NULL ||                                 \
              RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {            \
            struct type* oleft;                                               \
            if ((oleft = RB_LEFT(tmp, field)))                                \
              RB_COLOR(oleft, field) = RB_BLACK;                              \
            RB_COLOR(tmp, field) = RB_RED;                                    \
            RB_ROTATE_RIGHT(head, tmp, oleft, field);                         \
            tmp = RB_RIGHT(parent, field);                                    \
          }                                                                   \
          RB_COLOR(tmp, field) = RB_COLOR(parent, field);                     \
          RB_COLOR(parent, field) = RB_BLACK;                                 \
          if (RB_RIGHT(tmp, field))                                           \
            RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;                 \
          RB_ROTATE_LEFT(head, parent, tmp, field);                           \
          elm = RB_ROOT(head);                                                \
          break;                                                              \
        }                                                                     \
      } else {                                                                \
        tmp = RB_LEFT(parent, field);                                         \
        if (RB_COLOR(tmp, field) == RB_RED) {                                 \
          RB_SET_BLACKRED(tmp, parent, field);                                \
          RB_ROTATE_RIGHT(head, parent, tmp, field);                          \
          tmp = RB_LEFT(parent, field);                                       \
        }                                                                     \
        if ((RB_LEFT(tmp, field) == NULL ||                                   \
             RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) &&             \
            (RB_RIGHT(tmp, field) == NULL ||                                  \
             RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) {            \
          RB_COLOR(tmp, field) = RB_RED;                                      \
          elm = parent;                                                       \
          parent = RB_PARENT(elm, field);                                     \
        } else {                                                              \
          if (RB_LEFT(tmp, field) == NULL ||                                  \
              RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {             \
            struct type* oright;                                              \
            if ((oright = RB_RIGHT(tmp, field)))                              \
              RB_COLOR(oright, field) = RB_BLACK;                             \
            RB_COLOR(tmp, field) = RB_RED;                                    \
            RB_ROTATE_LEFT(head, tmp, oright, field);                         \
            tmp = RB_LEFT(parent, field);                                     \
          }                                                                   \
          RB_COLOR(tmp, field) = RB_COLOR(parent, field);                     \
          RB_COLOR(parent, field) = RB_BLACK;                                 \
          if (RB_LEFT(tmp, field))                                            \
            RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;                  \
          RB_ROTATE_RIGHT(head, parent, tmp, field);                          \
          elm = RB_ROOT(head);                                                \
          break;                                                              \
        }                                                                     \
      }                                                                       \
    }                                                                         \
    if (elm) RB_COLOR(elm, field) = RB_BLACK;                                 \
  }                                                                           \
                                                                              \
  struct type* name##_RB_REMOVE(struct name* head, struct type* elm) {        \
    struct type *child, *parent, *old = elm;                                  \
    int color;                                                                \
    if (RB_LEFT(elm, field) == NULL)                                          \
      child = RB_RIGHT(elm, field);                                           \
    else if (RB_RIGHT(elm, field) == NULL)                                    \
      child = RB_LEFT(elm, field);                                            \
    else {                                                                    \
      struct type* left;                                                      \
      elm = RB_RIGHT(elm, field);                                             \
      while ((left = RB_LEFT(elm, field))) elm = left;                        \
      child = RB_RIGHT(elm, field);                                           \
      parent = RB_PARENT(elm, field);                                         \
      color = RB_COLOR(elm, field);                                           \
      if (child) RB_PARENT(child, field) = parent;                            \
      if (parent) {                                                           \
        if (RB_LEFT(parent, field) == elm)                                    \
          RB_LEFT(parent, field) = child;                                     \
        else                                                                  \
          RB_RIGHT(parent, field) = child;                                    \
        RB_AUGMENT(parent);                                                   \
      } else                                                                  \
        RB_ROOT(head) = child;                                                \
      if (RB_PARENT(elm, field) == old) parent = elm;                         \
      (elm)->field = (old)->field;                                            \
      if (RB_PARENT(old, field)) {                                            \
        if (RB_LEFT(RB_PARENT(old, field), field) == old)                     \
          RB_LEFT(RB_PARENT(old, field), field) = elm;                        \
        else                                                                  \
          RB_RIGHT(RB_PARENT(old, field), field) = elm;                       \
        RB_AUGMENT(RB_PARENT(old, field));                                    \
      } else                                                                  \
        RB_ROOT(head) = elm;                                                  \
      RB_PARENT(RB_LEFT(old, field), field) = elm;                            \
      if (RB_RIGHT(old, field)) RB_PARENT(RB_RIGHT(old, field), field) = elm; \
      if (parent) {                                                           \
        left = parent;                                                        \
        do {                                                                  \
          RB_AUGMENT(left);                                                   \
        } while ((left = RB_PARENT(left, field)));                            \
      }                                                                       \
      goto color;                                                             \
    }                                                                         \
    parent = RB_PARENT(elm, field);                                           \
    color = RB_COLOR(elm, field);                                             \
    if (child) RB_PARENT(child, field) = parent;                              \
    if (parent) {                                                             \
      if (RB_LEFT(parent, field) == elm)                                      \
        RB_LEFT(parent, field) = child;                                       \
      else                                                                    \
        RB_RIGHT(parent, field) = child;                                      \
      RB_AUGMENT(parent);                                                     \
    } else                                                                    \
      RB_ROOT(head) = child;                                                  \
  color:                                                                      \
    if (color == RB_BLACK) name##_RB_REMOVE_COLOR(head, parent, child);       \
    return (old);                                                             \
  }                                                                           \
                                                                              \
  /* Inserts a node into the RB tree */                                       \
  struct type* name##_RB_INSERT(struct name* head, struct type* elm) {        \
    struct type* tmp;                                                         \
    struct type* parent = NULL;                                               \
    int comp = 0;                                                             \
    tmp = RB_ROOT(head);                                                      \
    while (tmp) {                                                             \
      parent = tmp;                                                           \
      comp = (cmp)(elm, parent);                                              \
      if (comp < 0)                                                           \
        tmp = RB_LEFT(tmp, field);                                            \
      else if (comp > 0)                                                      \
        tmp = RB_RIGHT(tmp, field);                                           \
      else                                                                    \
        return (tmp);                                                         \
    }                                                                         \
    RB_SET(elm, parent, field);                                               \
    if (parent != NULL) {                                                     \
      if (comp < 0)                                                           \
        RB_LEFT(parent, field) = elm;                                         \
      else                                                                    \
        RB_RIGHT(parent, field) = elm;                                        \
      RB_AUGMENT(parent);                                                     \
    } else {                                                                  \
      RB_ROOT(head) = elm;                                                    \
    }                                                                         \
    name##_RB_INSERT_COLOR(head, elm);                                        \
    return (NULL);                                                            \
  }                                                                           \
                                                                              \
  /* Finds the node with the same key as elm */                               \
  struct type* name##_RB_FIND(struct name* head, struct type* elm) {          \
    struct type* tmp = RB_ROOT(head);                                         \
    int comp;                                                                 \
    while (tmp) {                                                             \
      comp = cmp(elm, tmp);                                                   \
      if (comp < 0)                                                           \
        tmp = RB_LEFT(tmp, field);                                            \
      else if (comp > 0)                                                      \
        tmp = RB_RIGHT(tmp, field);                                           \
      else                                                                    \
        return (tmp);                                                         \
    }                                                                         \
    return (NULL);                                                            \
  }                                                                           \
                                                                              \
  struct type* name##_RB_NEXT(struct type* elm) {                             \
    if (RB_RIGHT(elm, field)) {                                               \
      elm = RB_RIGHT(elm, field);                                             \
      while (RB_LEFT(elm, field)) elm = RB_LEFT(elm, field);                  \
    } else {                                                                  \
      if (RB_PARENT(elm, field) &&                                            \
          (elm == RB_LEFT(RB_PARENT(elm, field), field)))                     \
        elm = RB_PARENT(elm, field);                                          \
      else {                                                                  \
        while (RB_PARENT(elm, field) &&                                       \
               (elm == RB_RIGHT(RB_PARENT(elm, field), field)))               \
          elm = RB_PARENT(elm, field);                                        \
        elm = RB_PARENT(elm, field);                                          \
      }                                                                       \
    }                                                                         \
    return (elm);                                                             \
  }                                                                           \
                                                                              \
  struct type* name##_RB_MINMAX(struct name* head, int val) {                 \
    struct type* tmp = RB_ROOT(head);                                         \
    struct type* parent = NULL;                                               \
    while (tmp) {                                                             \
      parent = tmp;                                                           \
      if (val < 0)                                                            \
        tmp = RB_LEFT(tmp, field);                                            \
      else                                                                    \
        tmp = RB_RIGHT(tmp, field);                                           \
    }                                                                         \
    return (parent);                                                          \
  }

#define RB_NEGINF -1
#define RB_INF 1

#define RB_INSERT(name, x, y) name##_RB_INSERT(x, y)
#define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y)
#define RB_FIND(name, x, y) name##_RB_FIND(x, y)
#define RB_NEXT(name, x, y) name##_RB_NEXT(y)
#define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF)
#define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF)

#define RB_FOREACH(x, name, head) \
  for ((x) = RB_MIN(name, head); (x) != NULL; (x) = name##_RB_NEXT(x))

#define RB_FOREACH_SAFE(x, name, head, y) \
  for ((x) = RB_MIN(name, head);          \
       ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); (x) = (y))

#endif /* _SYS_TREE_H_ */
